[R-sig-ME] ML vs. REML to find a parsimonious mixed model

[Maarten Jung]

I want to use LRTs via anova() on fitted linear mixed models (merMod
objects) to find a parsimonious mixed model containing only variance
components supported by the data (e.g. Matuschek et al. 2017 [1], Bates et
al. 2015 [2]).
In this situation my focus is *only on the reduction of the random effects
part* of the models.
The aforementioned papers use ML instead of REML estimation within this
process. Douglas Bates seems to prefer ML model comparison due to the
skewed nature of the distribution of variance estimators [3] and the user
Wolfgang states that "the ML estimator usually has lower mean-squared error
(MSE) than the REML estimator" [4]. However, literally every textbook I
know suggests using REML estimation when comparing mixed models that differ
only in their random effect parts.

What would you suggest in this particular situation? ML or REML?

Best regards,
Maarten

[1] https://arxiv.org/abs/1511.01864
[2] https://arxiv.org/abs/1506.04967
[3] https://stat.ethz.ch/pipermail/r-sig-mixed-models/2015q3/023750.html
[4] https://stats.stackexchange.com/a/48770

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